Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615733 | Journal of Mathematical Analysis and Applications | 2014 | 10 Pages |
Abstract
We study the problem (âÎ)su=λeu in a bounded domain ΩâRn, where λ is a positive parameter. More precisely, we study the regularity of the extremal solution to this problem. Our main result yields the boundedness of the extremal solution in dimensions nâ¤7 for all sâ(0,1) whenever Ω is, for every i=1,...,n, convex in the xi-direction and symmetric with respect to {xi=0}. The same holds if n=8 and sâ³0.28206..., or if n=9 and sâ³0.63237.... These results are new even in the unit ball Ω=B1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xavier Ros-Oton,